If an argument is invalid, then there is an interpretation where all the premises are true and the conclusion is false. So If the conclusion is a tautology, the argument must be valid since the conclusion can’t be false under any interpretation. Thank you for your answer.Jul 7, 2015
Can an invalid argument have a tautology as a conclusion?
Therefore, if the premises of a propositionally valid argument are tautologies, then its conclusion must be a tautology as well.
No propositionally valid argument can have a contradiction as a conclusion.
What is an invalid argument with a true conclusion?
The conclusion is actually true but this fact does NOT follow from the claim that the premises are true. We can imagine a fantasy in which the premises are true but the conclusion is still false.
Is a valid argument always a tautology?
It is not originally defined in the context of premise-conclusion as you said. However, it can be proven that tautological sentences as defined previously is always the ‘true conclusion’ of any argument regardless of truth of the premises. Therefore, tautology is always valid.
Why is the conclusion valid or invalid it is invalid?
A deductive argument is said to be valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. Otherwise, a deductive argument is said to be invalid.
What does an invalid argument mean?
Invalid: an argument that is not valid. We can test for invalidity by assuming that all the premises are true and seeing whether it is still possible for the conclusion to be false. If this is possible, the argument is invalid.